Abstract: A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the pressure at any point. Such solutions are called Gavrilov flows. Local structure of a Gavrilov flow { is} described in terms of geometry of isobaric hypersurfaces. In the 3D case, we obtain a system of PDEs for an axisymmetric Gavrilov flow and find consistency conditions for the system. Two numerical examples of axisymmetric Gavrilov flows are presented: with pressure function periodic in { the} axial direction, and with isobaric surfaces diffeomorphic to { the} torus

Cite: Sharafutdinov V.A. , Rovenski V.Y.
Gavrilov steady flows of ideal incompressible fluid
Quasilinear Equations, Inverse Problems, and Applications - 2022 22-26 Aug 2022